1. Field
The present invention relates to a method and apparatus for ultra fast symmetry and SIMD based projection-backprojection for 3D PET image reconstruction. More specifically, the present invention relates to a method and apparatus based on the symmetry properties of the projection and backprojection processes, especially in the 3D OSEM algorithm that requires a plurality of projections and back-projections.
2. Background
There has been a remarkable progress in PET development over the recent years, especially in the areas of hardware, software and computer implementation of image reconstruction. Recent developments in PET scanners (e.g., HRRT (High Resolution Research Tomograph) developed by CTI (now Siemens)) allow greatly enhanced resolution and sensitivity. In such PET scanners, the amount of collected coincidence line data contains more than 4.5×109 coincidence lines of response generated by as many as 120,000 nuclear detectors. Such large amount of data and the reconstruction of this data set pose to be a real problem in HRRT. That is, they pose to be major problems in achieving further developments and applications of high resolution PET scanners. Thus, in such types of scanners, obtaining one set of reconstructed images often requires many hours of image reconstruction. For example, in HRRT with full data collection in normal brain scans (using SPAN 3), the image reconstruction time is almost eighty minutes. This makes it practically impossible to attempt any list mode based dynamic imaging since the image reconstruction time takes many days (as long as 43 hours or more for 32 frame dynamic image reconstruction).
In general, tomographic images can be reconstructed by two approaches, one being an analytic method and the other being an iterative approach. PET scanners of different types were developed in the mid 1970's and the application of various tomographic image reconstruction techniques was naturally introduced in the field. In case of an analytic approach such as backprojection and filtering or filtered back-projection (FB), an artifact known as a streak artifact is frequently generated. This is especially true when the detector arrangements are not uniform such as in the case of HRRT (e.g., Siemens' High Resolution Research Tomograph) where the detectors are arranged in a set of blocks in an octagonal shape. These types of detector arrangements often involve missing data due to the gaps between the blocks and result in a severe streak artifact in the case of the FB technique. Therefore, alternative approaches such as an EM (Expectation Maximum) algorithm have been sought. Generally, the EM approach requires several steps in the reconstruction process, the two major steps of which are: projection (forward projection) to create projection data from the image or object and backprojection into the image domain for the final image reconstruction. In the EM algorithms, these two processes are repeated until satisfactory images are obtained. Obviously, these repeated projection and backprojection processes are time consuming and have been the major drawback of the EM approach compared to straight filtered backprojection (FB) algorithm. In addition, in case of 3D image reconstruction, the computational burden increases out of proportion due to the astronomical increases in the coincidence lines or the line of responses (LOR). This is a major stumbling block in the daily operation of high resolution PET scanners. Thus, there is a strong need for improving the computational speed or the reconstruction time in EM approaches, especially with high end PET scanners such as HRRT.
Projection methods usually employ a system matrix, which is determined by the geometric factor of the scanner. As the resolution of the PET image improves and the number of slices increases, the size of the matrix is also increased drastically in proportion to the increases in LORs, thus resulting in not only the need for a large memory but also the total computation time. Current HRRT, for example, requires nearly eighty minutes of reconstruction time, in addition to the generation of sinograms and appropriate data streaming processes such as attenuation, random and scatter corrections, a set of precursors to the reconstruction processes. To remedy the computational burden of image reconstruction, a number of alternative proposals such as linear integration have been proposed, as well as the use of multiple CPUs or a cluster computer system approach. Most of the techniques, however, are not practically useful since such cluster computing requires a large data transfer time, although the overall computation is faster than a single unit.
Obtaining or generating projection data can be divided into two categories, namely, ray-driven method and pixel-driven method. The ray-driven method calculates the linear integration directly along the ray path connecting the centers of the two opposite detector cells, whereas the pixel-driven method calculates the linear integration along the ray path centered around an image pixel for the entire projection angles. The ray-driven method is often used in projection, while pixel-driven method is used in backprojection.
In early reconstruction techniques, projection was obtained by weighing the ray passing through the areas of pixels with the assumption that the ray path is a strip with a finite width. It, however, involves a large amount of computation as well as the storage of a large number of matrix or data. Concurrently, Shepp and Logan proposed a simple and computationally efficient algorithm, which requires computing the length of the ray path intersecting with each pixel (instead of the areas).
To speed up the computation, there have been a number of attempts to reduce the reconstruction time. An incremental algorithm has also been developed in which the symmetric property between the neighboring pixels is considered to calculate the position of intersection of a ray. This idea was expanded to 3D reconstruction in cylindrical geometry using oblique rays. In 3D form with a multi-ring system such as HRRT, it became apparent that true 3D approaches will be required to fully utilize the oblique rays to thereby improve the statistics of the image.